Power spectrum and detrended fluctuation analysis: Application to daily temperatures

The variability measures of fluctuation analysis (FA) and detrended fluctua tion analysis (DFA) are expressed in terms of the power spectral density an d of the autocovariance of a given process. The diagnostic potential of the se methods is tested on several model power spectral densities. In particul ar we find that both FA and DFA reveal an algebraic singularity of the powe r spectral density at small frequencies corresponding to an algebraic decay of the autocovariance. A scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by DFA than by FA. We apply FA and DFA to ambient temperature data from the 20th century with th e primary goal to resolve the controversy in Literature whether the low fre quency behavior of the corresponding power spectral densities are better de scribed by a power law or a stretched exponential. As a third possible mode l we suggest a Weibull distribution. However, it turns out that neither FA nor DFA can reliably distinguish between the proposed models.